1. Field of the Invention
The invention relates to a method for constructing a model representative of a heterogeneous medium such as the subsoil, described by several parameters (which can be physical quantities or combinations of physical quantities) from data expressed in different time scales.
2. Description of the Prior Art
The following documents, mentioned in the description hereafter, illustrate the state of the art:    Aki, K., and Richards, P. G., 1980, Quantitative Seismology: Theory and Method, Vol.1: W.H. Freeman and Co    De Nicolao, A., Drufuca, G., and Rocca, F., 1993, Eigenvalues and eigenvectors of Linearized Elastic Inversion: Geophysics, 58, 670-679.    Gaiser, J. E., 1996, Multicomponent Vp/Vs Correlation Analysis: Geophysics, 61, 1137-1149.    Garotta, R., Granger, P-Y., and Dariu, H., 2000, Elastic Parameter Derivations from Multi-component Data, 70th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 154-157.    Lebrun, D., Richard, V., Mace, D., and Cuer, M., 2001, SVD for Multi-Offset Linearized Inversion: Resolution Analysis in Multicomponent Acquisition: Geophysics, 66, 871-882.    Tonellot, T., Macé, D., Richard, V., and Cuer, M., 2001, Joint Stratigraphic Inversion of Angle-Limited Stacks, 71th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 227-230.
In general terms, inversion is a technique allowing estimation of a model described by one or more parameters from indirect data. This technique is generally used when the parameters cannot be directly measured. This technique implies that one knows how to solve the problem of predicting the data when the parameters of the model are known (modelling allowing obtaining data referred to as synthetic data).
This is for example the case within the context of oil exploration where geological and petrophysical data characterizing a three-dimensional reservoir where only seismic data can generally be measured on a large scale are sought. In this context, the purpose of inversion is to determine parameters such as the impedances in relation to P waves or S waves, or the density, from seismic data coming from waves emitted in the medium by a seismic source. These waves are propagated in the subsoil and reflected on the medium discontinuities. They are recorded by pickups coupled with the underground formation and collected by an acquisition device. The seismic data used within the context of the description of the method thus contain information on the amplitude variation with the offset (source-receiver distance), that is with the incidence angle; they are referred to as prestack seismic data. Several wave types are propagated in an elastic medium. P waves (compressional waves or longitudinal waves) which correspond to a displacement in the direction of propagation and S waves (shear waves or transverse waves) which correspond to a displacement in a plane perpendicular to the direction of propagation and are not propagated in a fluid medium can be mentioned from among the most commonly used waves in the petroleum industry. These P and S waves are propagated at different velocities, velocity Vp of the P waves being higher than velocity Vs of the S waves. They reflect at the subsoil discontinuity interfaces and are recorded by the acquisition device. P waves can reflect in waves of the same type (PP reflections) or in waves of the other type (PS reflections). Terrestrial acquisition techniques and new marine acquisition techniques, for which the receivers are laid on the sea bottom and record the 3 displacement components (x,y,z) (multicomponent seismic data), allow the P and S waves reflected in the subsoil to be directly recorded. PP reflections, referred to as PP data, correspond to the record of a signal (seismogram) coming from waves transmitted in P type waves and reflected in P type waves in the subsoil. The amplitude of this signal is variable as a function of the time referred to as PP time. Similarly, PS reflections, referred to as PS data, correspond to the record of a signal coming from waves transmitted in P type waves and reflected in S type waves in the subsoil. The amplitude of this signal is variable as a function of the time referred to as PS time. The P and S waves being propagated at different velocities, a single geologic reflector will thus correspond to a signal variation at a time PP and at a time PS, these times being different. Besides, since these two signal variations correspond to reflections of different types, they have different values.
In the case of a medium such as the subsoil, the descriptive physical quantities are generally the impedance thereof in relation to these P waves or S waves, or its density. It is clear that the larger the number of physical quantities available to characterize the medium, the better the medium is described. This is why, in the petroleum industry, it has become equally important to estimate the P impedances and the S impedances. Each of these two physical quantities contains different information, which is necessary to correctly characterize a reservoir.
From the PP data, it is possible to carry out an inversion allowing estimation of the P impedances, the S impedances and the density. This is also the case with the PS data. However, several authors (De Nicolao et al., 1993; Lebrun et al., 2001) showed that, among the three parameters conventionally used and mentioned above, the P impedance (or more precisely its relative variation)
      Δ    ⁢                  ⁢    Ip    Ipis the best determined parameter from the PP data; on the other hand, the confidence that one can have in the relative variation of the S impedance is more limited and depends on factors such as the noise level, the range of incidence angles available and the errors on determination of the velocity model. However, if PS data are available, it is possible to reliably estimate the relative variation of the S impedance, hence an ever-growing interest in the acquisition and processing of multicomponent seismic data. As for density, it is difficult to estimate whatever the type of data used.
In the petroleum industry, inversion methods were developed, allowing accounting for single-component seismic data, corresponding to a given reflection type, direct data and geologic data on the subsoil. An a priori model (1D, 2D or 3D) of one or more parameters characteristic of the medium is constructed by interpretation of the known direct or indirect data, and covariance operators describing the uncertainties on this a priori model and the uncertainties on the indirect data recorded are defined. The starting point is from an initial model (the a priori model for example) and synthetic seismograms which constitute the response of the model are calculated. They are compared with the real seismograms obtained by seismic exploration and the differences observed are minimized step by step according to norms associated with the covariance operators selected as a function of an evaluation of the uncertainties on the a priori model and the seismic records.
The various known approaches differ notably in the number of parameters describing the medium, the dimension of the a priori model, and the abundance of possibilities provided when taking into account the uncertainty parameters. They consist in obtaining the optimum model minimizing a cost function, the sum of a cost function referred to as seismic, and of a cost function referred to as geologic. The seismic cost function represents the difference (in the sense of the norm induced by the covariance operator relative to the data) between the observed data (real seismograms) and the synthetic data associated with the current model. The geologic cost function measures the difference between the current model and the a priori model (in the sense of the norm induced by the covariance operator relative to the medium).
There are methods for estimating several parameters in a medium. Among these approaches is the method described in French Patent 2,800,473 filed by the Assignee, which allows obtaining an optimum model in 2 or 3 dimensions (2D or 3D), described by several parameters from indirect data corresponding to a single type of data (PP for example).
When several types of data are available (PP and PS for example), it is necessary to be able to invert the data jointly so as to take advantage of the information contained in the P impedance estimated from the PP data and in the S impedance estimated from the PS data. The difficulty of the problem lies in the fact that, the PP and PS data being supplied at different time scales (the P and S velocities are different), a solution has to be found to associate with precision the events corresponding to a single geologic reflector; this amounts to estimating the ratio of the P and S velocities, denoted by γ.
Two types of approach can be considered for jointly inverting prestack multicomponent seismic data.
The first approach first estimates the P and S velocity models (by migration and focussing analysis for example) and in taking, as data of the joint inversion, the results (expressed in depth) of a prestack depth migration. This approach is attractive but remains delicate because sufficiently precise P and S velocities have to be estimated.
The second approach considers the results of the time migration as inputs for the joint inversion and thus has to solve the crucial problem of matching the arrival times of the PP and PS reflections. It is in this context that the method according to the invention should be seen.
Various matching techniques, directly from the PP and PS data, exist (Gaiser, 1996) but they implicitly presuppose that the contrasts of the P and S impedances are similar or at least have like signs, which is not always the case, in particular at the reservoir level. In Garotta et al.'s approach (2000), the amplitudes of the P and S data, in a lateral position and at a given time (but for different incidence angles), are used to calculate the conventional AVO (Amplitude Versus Offset) attributes by means of linear regression methods:    the ordinate at the PP origin, referred to as PP “intercept” and expressed in PP time,    the PP “gradient” expressed in PP time,    the PS “gradient” expressed in PS time.
The relative variation of ratio (γ) of the P and S velocities can then be expressed by a formula involving γ, the PP intercept, the PP gradient and the PS gradient converted to PP time using γ. On the other hand, for a given association of the PP and PS times, the corresponding γ can be calculated. Ratio γ calculated by Garotta et al. is the ratio which minimizes the difference between the relative variation of γ from the propagation times and the relative variation of γ from the AVO attributes.